(As required by the Governor of the State of California) Quantum Hall Effect Jesse Noffsinger Group Meeting Talk (As required by the Governor of the State of California) April 17, 2007

Classical Hall Effect B +++++++++++++++++++ Ex, jx VH Ey Experimental Values* B Metal RH (-1/nec) Li 0.8 Na 1.2 Rb 1.0 Ag 1.3 Be -0.2 +++++++++++++++++++ Ex, jx VH Ey - - - - - - - - - - - - - - - - - - *Ashcroft and Mermin

Integer QHE Discovered in 1980, Nobel Prize awarded to von Klitzing in 1985 aa SEM image of a Hall bar* *Georgia Tech physics website

Quantum Mechanical Description Landau Gauge:

Degeneracy of Landau Levels Each wavefunction is centered at Energy DOS: Increasing B

Only extended states carry current! Impurity Effects Isolated -fn potential localizes one extended state Only extended states carry current! Extended States E Localized States DOS

The Laughlin Argument for the Integer Hall effect Form a closed loop w/ Hall bar Change the flux through the loop by one quanta: No change can take place in the bulk – move one electron to the other edge p must be an integer

Fractional QHE Cannot be explained in terms of free electrons Filling factor is a rational fraction Cannot be explained in terms of free electrons

Composite Fermion Picture Electrons IQHE Composite Fermions FQHE Fractional Hall effect encompasses states with filling factors: Composite fermions can be viewed as electrons with attached flux quanta is screened to

Lowest Landau level splitting for composite fermions Energy v=1 lowest Landau Level splits into levels separated by The fractional filling of electrons is really the integral filling of composite fermions

Conclusion Integral Quantum Hall effect can be accurately modeled as a non-interacting electron gas in a magnetic field The Fractional Quantum Hall effect involves composite fermion quasi-particles which are electrons with attached flux quanta